Kennison attended Washington-Marion High School in Lake Charles, Louisiana, and was a star in both football and track. In football, as a senior, he was a Parade All-American despite playing only six games. He finished his senior year with 27 receptions for 497 yards (18.4 yards per reception avg.). As a junior, he hauled in 59 receptions for 1,205 yards (an average of 20.4 yards per reception) and 23 touchdowns. For his efforts, he was the first person in his school's history to have his number retired.

Kennison was selected 18th overall by the St. Louis Rams in the 1996 NFL Draft, a draft which was remarkably deep in wide receivers. On July 30, 1996, Kennison, signed a four-year, $6 million deal with a $2 million signing bonus. His first season with the Rams was excellent, as he finished second to Terry Glenn in yards and receptions for rookies, and led the rookie wide receiver class in touchdowns. It was noted regularly at the time that Kennison and Glenn had outproduced number one overall pick Keyshawn Johnson. He also was selected as an alternate to the Pro Bowl. His 1997 and 1998 seasons with the Rams were far less productive, as he battled nagging injuries in a lackluster Rams offense.

On February 18, 1999, Kennsion was traded to the New Orleans Saints for a second-round draft pick in the 1999 NFL Draft. Saints coach Mike Ditka said, "Our goal as coaches is to get Eddie back to the form he displayed as a rookie". In 1999 he led the team in receptions and yards. This Saints team was notable for using four different startingquarterbacks over the course of the year as they struggled to a 3–13 record.

On February 22, 2000, the Saints traded Kennison to the Chicago Bears for a fifth-round pick in the 2000 NFL Draft. "(Kennison) gives us another speed guy, and that's something you can't have enough of", his new coach said. With the Bears he continued a pattern of unspectacular but reliable production. He finished second on the team to Marcus Robinson in receiving yards, and tied Robinson for the team lead in receptions. His salary for the 2000 season was $1.02 million.

On April 5, 2001, Kennison signed a two-year, $1.8 million deal that includes a $500,000 signing bonus with the Denver Broncos. He earned a starting role out of training camp, but after eight unproductive games, Kennison requested to be released from the team only a few hours before a game in which he was scheduled to start. He stated at the time he had "lost his love for the game", and as a result Kennison retired and was released on November 15, 2001. The loss of Kennison, along with a severe injury to Ed McCaffrey decimated a once dominant Broncos corps of wide receivers.

Kennison unexpectedly resurfaced less than a month later, signing with the Broncos' arch-rival Kansas City Chiefs on December 3, 2001, to the outrage of Broncos coach Mike Shanahan.[2] Kennison's new contract was for two-years and $4.5 million with $3.2 guaranteed. Kennison would lead the Chiefs in receiving his first game as a starter.

On January 3, 2003, Kennison signed a six-year $9 million contract extension with the Chiefs. As a member of the Chiefs, from 2002 to 2006 Kennison averaged 59 receptions, 961 yards, and 5 touchdown catches during this span.

In 2007, Kennison sustained a severe hamstring injury on the first play of the regular season, and was plagued by the injury for the remainder of the season. He was released the following offseason on February 26, 2008.

Kennison was re-signed by the Rams on September 9, 2008.[3] The team released rookie linebackerDavid Vobora to make room for Kennison.

Kennison was released by the Rams on October 7, then signed again just hours later after it was learned Rams wide receiverDane Looker was not yet cleared to play after suffering a concussion.[4] He was released again on October 22.